Zelevinsky Duality on Basic Local Shimura Varieties

2021/09/02 by Linus Hamann, Hamann, Linus
Mathematics · Medicine · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Phytoestrogen effects and research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2109.01213

openalex publication_date 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple proof of a general result describing the action of the Zelevinsky involution on the cohomology of certain basic local Shimura varieties, using the machinery of Fargues-Scholze. As an application, we generalize earlier results of Fargues and Mieda on the action of the Zelevinsky involution on the cohomology of GL_n and GSp₄ type basic local Shimura varieties, respectively.

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